Welsh or Scottish river to carry on intensely (6)
I believe the answer is:
deeply
'intensely' is the definition.
(I've seen this before)
'welsh or scottish river to carry on' is the wordplay.
I cannot quite see how this works, but
'river' could be 'dee' (River Dee) and 'dee' is found within the answer.
'carry on' could be 'ply' (ply can mean to work continually at something) and 'ply' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for deeply that I've seen before include "With profundity" , "With intense feeling" , "In a profound way" , "fathoms down?" , "Thoroughly" .)