They're 2 I struggled with as well.
13a - First 3 letters are "operative regularly" + first 2 letters of a 3 letter "was taken in" as in 'conned' or 'fell for'.
23a - First 4 letter letters "fancy" then a 4 letter "interest" (I wouldn't have associated this common word with interest in a million years but Chambers gives it) around single letter "Henry".