Question: - Can I practice by putting on the green of the hole that I have just played?
Although the R&A Rules of Golf state that a player may not make a practice stroke during the play of a hole there are exceptions. You may practice chipping or putting on the putting green of the hole last played. (R&A Rule 7-2 (a)).
This rule applies to both Matchplay and Stroke Play.
This type of practice, although allowed by the rules of golf, is not encouraged as it can easily delay play. (R&A Rules of Golf 6-7 Note 1)
Playing without undue delay does not just mean the playing of a hole it also covers the time taken between the last green played and playing from the next tee.
So any practice must not delay play.
Always remember that the Competitions Committee are able to impose penalties for slow play.