Dad holds up an immobile creature (4)
I believe the answer is:
pupa
'an immobile creature' is the definition.
'pupa' can be an answer for 'creature' (pupa is a kind of creature). I'm not certain of the 'an immobile' bit.
'dad holds up' is the wordplay.
'dad' becomes 'pa' (both can mean one's father).
'holds' is an insertion indicator.
'pa' enclosing 'up' is 'PUPA'.
Can you help me to learn more?
(Other definitions for pupa that I've seen before include "One is growing" , "creepy-crawly" , "appearance of immaturity" , "middle stage" , "So peacock may have appeared" .)