Re-entry in Tbilisi after a passport renewal

So my case is a bit different. Looking at the number of posts saying students are getting denied into entering the country at the airports is scaring me.

My trc’s getting expired in September so according to the 40 days rules, I should be applying for its renewal in mid July. But I have to travel in the first week of July to get my passport renewed as well. The officials said I can apply for the trc renewal in less than 90 days and can travel back till my trc expires. But with a new trc in process and a new passport, will I be allowed to enter again?