I'd lifted the front part of a seat (5)
I believe the answer is:
divan
'seat' is the definition.
(divan is a kind of seat)
'i'd lifted the front part' is the wordplay.
'lifted' shows that the letters should be reversed in order (going up in down clue).
'the front part' becomes 'van' (van can mean the front of something).
'id' in reverse letter order is 'di'.
'di'+'van'='DIVAN'
'of a' is the link.
(Other definitions for divan that I've seen before include "Couch - bed" , "Viand (anag.)" , "Long backless sofa" , "Sort of bed" , "resting place" .)