Not sure about that - a non-UK TRE conducting an LPC or otherwise for a UK licence holder post Brexit wouldn't be possible without change of SOLI. The base document would have to be Part-FCL so in this case, a Part-FCL CPL/IR with ATPL TK credit would be required, as a UK issued Part-FCL licence will become a UK national one post departure. This might offer some respite though
Regulation (EU) 2019/502