Agriculturist losing rights to celebrity (4)
I believe the answer is:
fame
'celebrity' is the definition.
(synonyms)
'agriculturist losing rights' is the wordplay.
'agriculturist' becomes 'farmer' (I've seen this before).
'losing' suggests deleting specific letters.
'rights' becomes 'rr'.
'farmer' with 'rr' removed is 'FAME'.
'to' acts as a link.
(Other definitions for fame that I've seen before include "14 [BOWIE] recorded this" , "Musical - stardom" , "Note" , "Celebrity; stage musical" , "Renown, celebrity" .)