Not reallly the automatic command I'm sure you're dreaming of but here is the best methodology I know to refine a tet mesh locally :
- Create skin elements around the solid mesh to refine using the Edge members command,
- Detele the solid mesh (Use the Previous button of the Selection Box),
- Refine the skin mesh on the "external faces" (not in the common boundary with the remaining tet mesh),
- Fill the skin refined mesh with tets using the Solid From Elements Command,
- Merge nodes between new and old mesh.
To refine the skin mesh, you may have to convert to linear elements (Modify / Update Elements / Linear parabolic Order) depending on the refining method (Commands from the Mesh / Editing for example).
You may also create surface from mesh (Geometry / Surface / From Mesh) before refining the skin elements to keep the original curvature by projecting news nodes.
The idea is this is easier to refine surface mesh than tet mesh even if this not completly automatic.
Hope this helps,