At Beachy Head, I had an offer (3)
I believe the answer is:
bid
'an offer' is the definition.
(bid is a kind of offer)
'at beachy head i had' is the wordplay.
'at' means one lot of letters go next to another.
'head' says to take the initial letters.
'i had' becomes 'i'd' (I'd).
The initial letter of 'beachy' is 'b'.
'b' put next to 'id' is 'BID'.
(Other definitions for bid that I've seen before include "Attempt, offer" , "Make offer for 20 Down" , "Tender (for work)" , "Try" , "Invite" .)