Parent dreadful at dancing, primarily (3)
I believe the answer is:
dad
'parent' is the definition.
(dad can informally mean father)
'dreadful at dancing primarily' is the wordplay.
'primarily' suggests taking the first letters.
The first letters of 'dreadful at dancing' is 'DAD'.
(Other definitions for dad that I've seen before include "Pa" , "Father, in short" , "Old man" , "Papa" , "Pop, pater" .)