Pay for enjoyable open day (4)
I believe the answer is:
fund
'pay for' is the definition.
(synonyms)
'enjoyable open day' is the wordplay.
'enjoyable' becomes 'fun' (fun means enjoyable or pleasing).
'open' says to take the initial letters (take the opening letter).
The initial letter of 'day' is 'd'.
'fun'+'d'='FUND'
(Other definitions for fund that I've seen before include "Stock, resources" , "Sum of money set aside for a purpose" , "Cash reserve" , "Sponsor" , "Reserve of money for future use" .)