Grave robber's first love gets a hat (8)
I believe the answer is:
'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'.
'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" .)