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 am not certain of the 'directly' bit.
'shame getting out of breath but' is the wordplay.
'shame' becomes 'pity' (synonyms).
'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 give a lot more credence to this answer).
'pity' going around '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" .)