Joke by one in senile dotage (4)
I believe the answer is:
gaga
'in senile dotage' is the definition.
(I've seen this before)
'joke by one' is the wordplay.
'joke' becomes 'gag' ('gag' can be a synonym of 'joke'**).
'by' means one lot of letters go next to another.
'one' becomes 'a'.
'gag'+'a'='GAGA'
(Other definitions for gaga that I've seen before include "In repetitive slang, senile or crazy" , "Barmy joke, third in cracker" , "In senile dotage" , "bananas" , "Lady < > in a senile" .)