Unconscious present influence that’s hidden (12)
I believe the answer is:
undercurrent
'influence that's hidden' is the definition.
'unconscious present' is the wordplay.
'unconscious' becomes 'under' (as in under anaesthetic).
'present' becomes 'current' (similar in meaning).
'under'+'current'='UNDERCURRENT'
(Other definitions for undercurrent that I've seen before include "Suppressed feeling" , "Flow hidden beneath surface" , "Riptide" , "Dangerous flow beneath sea surface" , "Sub-surface flow" .)