Like something that matters about eastern part of Med (8)
I believe the answer is:
relevant
'like something that matters' is the definition.
'about eastern part of med' is the wordplay.
'about' becomes 're' (regarding).
'eastern part of med' becomes 'levant' (the Levant is a Mediterranean region).
're'+'levant'='RELEVANT'
(Other definitions for relevant that I've seen before include "Applicable" , "Significant" , "Material" , "Closely connected (to the matter in hand)" , "To the point" .)