We investigate the prospect of discovering the Flavour Changing Neutral Current (FCNC) tqZ couplings via two production processes yielding trilepton signals: top quark pair production pp → t(t) with one top quark decaying to the Z boson and one light jet and the anomalous single top quark plus Z boson production process pp → tZ.We study these channels at various successors of the Large Hadron Collider (LHC),i.e.,the approved High-Luminosity LHC (HL-LHC) as well as the proposed High-Energy LHC (HE-LHC) and Future Circular Collider in hadron-hadron mode (FCC-hh).We perform a full simulation for the signals and the relevant Standard Model (SM) backgrounds and obtain limits on the Branching Ratios (BRs) of t → qZ (q =u,c),eventually yielding a trilepton final state through the decay modes t → bW+ → b(l)+v(l) and Z → (l)+(l)-.The upper limits on these FCNC BRs at 95％ Confidence Level (CL) are obtained at the HL-LHC with √s =14 TeV and 3 ab-1,at the HE-LHC with √s =27 TeV and 15 ab-1,and at the FCC-hh with √s =100 TeV and 30 ab-1.