What options are available for gap between interior door frame and wall?
For small gaps between wooden trim such as doorframes and plastered walls I use a "Flexible gap filler" - available at any DIY store. Spending a few minutes reading the containers carefully and asking store assistants will get you a product you can try.

Description from a randomly selected product


  This flexible filler achieves a white crack-free fill between two surfaces where movement can occur. Controlled application is ideal for long linear gaps.
  
  
  For flexible, crack-free filling between two surfaces where movement can occur.
  Easily controlled application for long linear gaps.
  For indoor and outdoor use.
  


Another one


  An acrylic filler for draught proofing and filling fine cracks. Can be sanded, overpainted or papered over. Solvent free formulation.
  
  
  Interior or Exterior Use: Interior
  Application Method: Knife
  Colour: White
  Size: 310 ml
  Type: Ready Mixed Filler 
  


It is often a good idea to rake out the corner first, to remove loose or weak paint. Then sand as necessary before cleaning and filling.