@yukinoh1989 Unfortunately you can’t change the resolution dynamically and keep what you’ve painted. You can change the resolution in the N-panel of the UV/Image Editor but it will erase any painted data.
Alternatively you can save your texture as an image file, open that file in Photoshop or Gimp or Krita, enlarge it, save it, reload that file back in Blender. But enlarging it will be blurry.
Typically I will paint a texture at 4096 x 4096 pixels to achieve details. I can always shrink it later no problem.