Bore a 1-inch-deep hole into a side of the loose newel post’s base using a hand drill and 1-inch-wide spade bit. Angle the drill bit lightly toward the framing of the first step behind the post, instead of drilling it straight.
Replace the 1-inch spade bit with a 7/32-inch drill bit. Using the 1-inch hole as an access hole, drill another hole through the newel post and into the stair framing. Replace the drill bit with a 5/16-inch drill bit and drive it through the hole in the newel post to create a wider clearance hole. However, do not extend this bit into the hole in the stair framing.
Insert a 5-inch-long, 5/16-inch-wide lag screw and 3/4-inch-wide washer into the post and tighten it with a ratchet wrench. This screw secures the newel post to the stair frame. Use a level to check that the newel post is plumb or repositioned, if required, so the level reads plumb before you tighten the screw all the way.
Measure and cut the pointed end of a dowel rod 1 inch in length. Insert this length into the 1-inch hole in the newel post and tap it gently to drive it all the way through.
Spread an even layer of wood putty over the plug with a putty knife. Scrape the surface of the putty with a knife until flush with the surrounding wood. Allow the putty to dry according to the time specified on the label directions.
Sand the dried putty with fine-grit sandpaper to smooth it. Wipe the surface of the newel post with a moist rag to remove residual dust. Paint or stain the putty so it blends with the surrounding newel post surface.