Dominant across old part of Yorkshire (10)
I believe the answer is:
overriding
'dominant' is the definition.
(similar in meaning)
'across old part of yorkshire' is the wordplay.
'across' becomes 'over' (synonyms).
'old part of yorkshire' becomes 'riding' (historical term for a region of Yorkshire).
'over'+'riding'='OVERRIDING'
(Other definitions for overriding that I've seen before include "taking precedence" , "most important" .)