There is much more certainty expressed about this in the gun press in the USA than in the Pakistani or Czech media, but it looks like Pakistan may have reached an understanding with CZ-UB for a next generation military rifle.
The Paki competition has been no secret, nor has their desire (1) to make the gun locally and (2) to be free to export it. Some manufacturers have hung up on the first condition, but the second has been more problematical: who wants to compete with his own design, manufactured by well-educated and skilled, but much less expensive, Pakistani labor? In addition, Pakistan, burned before by on-again, off-again American sanctions, doesn’t trust American suppliers. Still, there have been a number of entries (alphabetically by manufacturer):
Beretta ARX-200 — Beretta is hungry for a high-profile sale of its decent rifle, which has not been able to break out of the pack on the international market. This was always considered a longshot entrant.
CZ-806 Bren2 — CZ-UB has also provided a previously unseen variant, the CZ 807 in 7.62 x 39 mm, for the Type 56-2 part of the contract, and is offering the 806 in 5.56 plus a variant in 7.62 NATO with 14″ or 16″ barrel. CZ’s production costs are low enough to make the Bren very competitive. 
FN-SCAR-H — adopting this rifle would be popular with the troops, but there may be cost issues. US SOF have used it for some years and opinions are split. FN could really use a major sale of this excellent weapon. The NATO 7.62 caliber is widely used by today’s Pakistan Army and this could directly replace the elderly G3s, whose design dates to the early 1950s (although HK roller-lock guns are still in production by POF).
Kalashnikov AK-103 — Kalashnikov Concern too could use a high-profile export sale, but having been burned in the past by global copying of Soviet-era Kalashnikov weapons without bourgeois capitalist royalties, they’re reluctant to bless a lower-cost producer to export their designs. (It may come down to royalty rates — and the degree to which the famously trusting Russians trust the famously upright Pakistanis). Another plus would be that most extant accessories like magazines and pouches work fine with the updated AK. The 7.62 x 39 Bren, on the other hand, requires a new, proprietary polymer magazine (although it should fit fine in most AK mag pouches).
Zastava M21 — The Croatian bullpup, another longshot, was eliminated early, but expect the Croats to keep showing up at competitions, and tweaking their firearm based on feedback. They also submitted a conventional layout carbine in 7.62 NATO, based on the former Yugoslav M76 sniper rifle (for which they did produce 7.62 versions for export, even though the native gun was in 7.92 x 57 mm).
POF and CZ-UB have, according to Pakistani and Czech media, reached a memorandum of understanding about co-production and ultimately Pakistani production of the CZ-UB design, which has been interpreted as a signal of a CZ win in the competition, but might not be that at all, but an earlier milestone — i.e., a co-production agreement if CZ wins.
The Nature of the Competition is Unclear
While the Pakistan Army wants to replace both its G3s and its Chinese Type 56-2 AKs, what isn’t clear is whether this is one competition for one rifle, or two competitions for two rifles, in two calibers. Both of the current rifles have their fans in the South Asian nation’s forces, the AK for its compactness and doglike reliability, and the G3 for its range and ability to digest less-than-perfect ammunition. But the last matters less as POF ammo QC has improved, and the Pakistan Army is professional enough to train with whatever it gets from its lords and betters, rifle-wise.
Some sources have already reported that the CZ 807 in 7.62 x 39 has won the nod to replace the AK, and that this gives the CZ 806 in 5.56 or the future 7.62 x 51 variant the inside track to replace the G3.
Having weapons chambered or both NATO and former ComBloc calibers has logistic consequences, but given that Pakistan can produce indigenous weapons and ammo in both calibers, it also has operational benefits. For example, Pakistani troops can interoperate with any conceivable ally (and they often do, as UN peacekeepers) without fretting about ammo supply.
The Threat Pakistan’s Generals See
While Pakistan has been engaged in bitter antiterrorist operations (and Pakistani politics is sufficiently complex that sometimes Pakistani officials find themselves on both sides of a fight), the Army’s focus is and has been since inception on war with India. Pakistan has fought major wars with India in 1947, 1965, and 1971, and limited wars in 1985 and 1999. Pakistan has also made an ally of China, with India allying with Russia, but Pakistani generals now fear a two-front war in the case of Chinese-Indian rapprochement, something made possible by Russian weakness and US abdication in the region. Thus, Pakistan weapons procurement is driven largely by the need to match India and exploit asymmetries to offset India’s demographic and economic superiority. The Pakistani service also knows its forces have come a long way since the US invaded Afghanistan next door, and would like to see their equipment improved to match — hence the timing of this planned move up from 1940s and 50s weapons designs.
For more information
The FireArm Blog: Pakistani POF tentative plans to produce CZ 806 Bren 2. This is the article that got us digging into foreign sources.
The FireArm Blog: First Look at 7.62×39 CZ Bren 2, More Details on Pakistani Trials Rifles. Earlier story.
Armadní Noviny (Army News, Czech Republic): Útočná puška CZ BREN 2: Nový přístup, nové myšlení (Assault Rifle CZ BREN 2: New Approach, New Ideas). Here’s a Google Translation. Note section on Pakistan.
Armadní Noviny (Army News): Útočná puška CZ BREN 2 pro pákistánskou armádu?
(Assault Rifle CZ BREN 2 for the Pakistani Army?). Here’s the Google Translation. If there’s enough demand we’d do a proper translation of these articles.
Thread at Defence.pk: Pakistan’s Service Rifle (G-3, Type-56) Replacement Competition 2016. (like any forum thread, it’s uneven, but it’s mostly Pakistanis interested in this commenting there, so there’s an insight you won’t get from Western discussions. Up to you how to weight it.
Thread at Defence Forum India: CZ BREN 807 win Pakistani tender to replace Type 56 Assault Rifles. (The early pages are quite informative, but with both Indian and Pakistani participants, it soon degenerates into trash talking).