Party record; first had one, followed by number of fish (7)
I believe the answer is:
dolphin
'fish' is the definition.
(dolphin is a kind of fish)
'party record first had one followed by number' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'record' becomes 'LP' (L-P is an example).
'first had' becomes 'h' (ist letter of 'had').
'one followed' says to put letters next to each other.
'by number' becomes 'in' (I am not sure about this - if you are sure you should believe this answer much more).
'do'+'lp'+'h'+'in'='DOLPHIN'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for dolphin that I've seen before include "Small (bottlenosed) whale" , "Sea-mammal" , "Sea mammal like large porpoise, friendly towards people" , "Small sociable whale" , "member in school" .)