Roman Catholic AnswerThere was no new "church of Trent". The Council of Trent was 19th of 21 general ecumenical councils of the Catholic Church, (not counting the Council of Jerusalem in the books of Acts):
First Ecumenical Council: Nicaea I (325)
Second Ecumenical Council: Constantinople I (381)
Third Ecumenical Council: Ephesus (431)
Fourth Ecumenical Council: Chalcedon (451)
Fifth Ecumenical Council: Constantinople II (553)
Sixth Ecumenical Council: Constantinople III (680-681)
Seventh Ecumenical Council: Nicaea II (787)
Eighth Ecumenical Council: Constantinople IV (869)
Ninth Ecumenical Council: Lateran I (1123)
Tenth Ecumenical Council: Lateran II (1139)
Eleventh Ecumenical Council: Lateran III (1179)
Twelfth Ecumenical Council: Lateran IV (1215)
Thirteenth Ecumenical Council: Lyons I (1245)
Fourteenth Ecumenical Council: Lyons II (1274)
Fifteenth Ecumenical Council: Vienne (1311-1313)
Sixteenth Ecumenical Council: Constance (1414-1418)
Seventeenth Ecumenical Council: Basle/Ferrara/Florence (1431-1439)
Eighteenth Ecumenical Council: Lateran V (1512-1517)
Nineteenth Ecumenical Council: Trent (1545-1563)
Twentieth Ecumenical Council: Vatican I (1869-1870)
Twenty-first Ecumenical Council: Vatican II (1962-1965)
All of these councils were councils called by the Holy Father and attended by as many bishops as he could get there. They were all guided by the Holy Spirit and approved by Rome so that their decisions are binding on all of Christ's Church. Each and everyone of them was called to deal with various heresies. Many of their decisions involved the first time a doctrine was actually "defined" for the simple reason that it was the first time it had seriously been called into question. There was no new church after Trent, just as there was no new church after Nicaea. Despite other opinions to the contrary, the Church of Rome was established by Christ and remained faithful to Him throughout the centuries. There is no "church of Trent".