Separate selection §, apply a subsurf modifier, join back (Ctrl+J) and fill the gap
or
For this particular scenario you could just try subdividing and then making the loops circular with loops tools addon
Not judging - well okay maybe a little.
Here’s a quick and dirty.
delete a vertex.
select the edge.
This pic shows a circularization, but you might as well wait until step 5… and you should actually first -
Subdivide it with two cuts(not one - you’ll see why later)!
circularize it. (looptools circle, or transform/sphere and then scale to zero)
extrude in place and scale down to give it a little edge support for smoothing. Except I didn’t do this in the pics… but you should. I did this in step 8 in a more difficult way.
make a face - this helps the extrusion but if you are axial you don’t need to because you will…
Extrude to the right length with two steps in between and then delete the face if there was one.
Grid fill. Yes one step tool for a complicated process - but you have to have an even number of verts.
Done, except I can’t sleep the sleep of the just if I don’t fix that topology (that’s why I did the 2 cut subdiv earlier, one cut generates pentagons, but two makes hexes which are easier to retopo).
Also, in theory, this complex approach will be moot after Open SubDiv arrives. I read this morning that things are progressing very nicely. Perhaps by the end of the year.