Criminal unionist, being more important, avoided broadcast (8)
I believe the answer is:
bigamist
'criminal unionist' is the definition.
(one making a criminal number of unions)
'more important avoided broadcast' is the wordplay.
I cannot really see how this works, but
'more' could be 'm' and 'm' is present in the answer.
'important' could be 'big' ('big' can be similar in meaning to 'important') and 'big' is found in the answer.
This may be the basis of clue (or it may be nonsense).
'being' acts as a link.
(Other definitions for bigamist that I've seen before include "Person who commits crime of marrying while still married to another" , "One who unlawfully marries a second wife" , "One with two other halves?" , "One married to two people at once" , "member of two unions" .)