Happy puppy initially let out (7)
I believe the answer is:
pleased
'happy' is the definition.
(similar in meaning)
'puppy initially let out' is the wordplay.
'initially' suggests taking the first letters.
'let out' becomes 'leased' (as in leasing or letting out property).
The first letter of 'puppy' is 'p'.
'p'+'leased'='PLEASED'
(Other definitions for pleased that I've seen before include "like Punch?" , "Euphoric" , "Happy, satisfied" , "Well satisfied" , "Grateful, delighted" .)