To be exact, the right one to dig up (5)
I believe the answer is:
rigid
'to be exact' is the definition.
(thesaurus)
'right one to dig up' is the wordplay.
'right' becomes 'r' (common abbreviation).
'one' becomes 'i' (Roman numeral).
'to' says to put letters next to each other.
'up' is a reversal indicator (in down clue: letters go upwards).
'dig' backwards is 'gid'.
'r'+'i'+'gid'='RIGID'
'the' acts as a link.
(Other definitions for rigid that I've seen before include "Uncompromising" , "Unable to bend" , "Stiff, unyielding" , "Firmly fixed" , "Frozen" .)