Grave robber's first love gets a hat (8)
I believe the answer is:
sombrero
'a hat' is the definition.
(sombrero is a kind of hat)
'grave robber's first love' is the wordplay.
'grave' becomes 'sombre' (I've seen this before**).
'first' suggests taking the first letters.
'love' becomes 'o' (In tennis, 'love' means 'zero').
The first letter of 'robbers' is 'r'.
'sombre'+'r'+'o'='SOMBRERO'
'gets' is the link.
(Other definitions for sombrero that I've seen before include "Hat for South American" , "Wide-brimmed 23" , "Wide-brimmed Mexican hat" , "Broad-brimmed Mexican hat" , "CLOTHING" .)