Shame getting out of breath, but it’s directly significant (5)
I believe the answer is:
pithy
'directly significant' is the definition.
'pithy' can be an answer for 'significant' (thesaurus). I'm not sure about the 'directly' bit.
'shame getting out of breath but' is the wordplay.
'shame' becomes 'pity' ('pity' can be a synonym of 'shame').
'getting out of' is an insertion indicator (to be outside something can mean to be around it).
'breath but' becomes 'h' (I can't justify this - if you can you should believe this answer much more).
'pity' enclosing 'h' is 'PITHY'.
'it's' acts as a link.
Can you help me to learn more?
(Other definitions for pithy that I've seen before include "Brief, to the point" , "Short and to the point" , "succinctly expressed" , "(Of language) terse, strongly expressive" , "Terse and vigorously expressive" .)