Catch up, admitting fine is minimal (5)
I believe the answer is:
token
'minimal' is the definition.
('token' can be similar in meaning to 'minimal')
'catch up admitting fine' is the wordplay.
'catch' becomes 'net' (netting is a kind of catching).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'admitting' means one lot of letters goes inside another.
'fine' becomes 'ok' ('OK' can be a synonym of 'fine').
'net' written backwards gives 'ten'.
'ten' enclosing 'ok' is 'TOKEN'.
'is' is the link.
(Other definitions for token that I've seen before include "Gift voucher - symbol" , "Voucher (for, eg, books)" , "Done for appearance's sake" , "Counter" , "without meaning it" .)