Branch dropped in river? That's a shame (4,2)
I believe the answer is:
dear me
'a shame' is the definition.
I know nothing about this answer so I cannot judge whether this works.
'branch dropped in river?' is the wordplay.
'branch' becomes 'arm' (synonyms).
'dropped in' means one lot of letters goes inside another.
'river?' becomes 'Dee' (River Dee).
'arm' put into 'dee' is 'DEAR ME'.
'that's' is the link.
Can you help me to learn more?
(Other definitions for dear me that I've seen before include "Mild expression of distress from expensive self" , "how distressing!" , "Expression of dismay" , "What a pity" , "how sad" .)