The longest time between two consecutive NHL playoff goals for a player is 11 years, which has been done by 5 players:
Craig Ludwig: 103 games apart, 4079 days
- 04/09/1988, Montreal @ Hartford
- 06/10/1999, Dallas vs Buffalo
James Patrick, 72 games apart, 4027 days
- 04/21/1990, NY Rangers vs Washington
- 04/30/2001, Buffalo vs Pittsburgh
Bob Goldham: 20 games apart, 4004 days
- 04/16/1942, Toronto at Detroit
- 04/02/1953, Detroit vs Boston
Walt McKechnie: 1 game apart (consecutive!), 3994 days
- 05/03/1968, Minnesota North Stars @ St. Louis
- 04/10/1979, Toronto @ Atlanta Flames
Mathieu Schneider, 35 games apart, 3962 days
- 06/05/1993, Montreal @ Los Angeles
- 04/10/2004, Detroit vs Nashville
10 years apart has been achieved by 14 players, 9 years by 12 players.
Looked up list of players who scored a goal in any year in the playoffs, copied all 9352 player-seasons to Excel, and then queried to see the longest time between consecutive seasons for a given player. Once I had the names, I looked them up to see the specifics on dates and games.
Here is the Hockey-Reference list of players who scored a playoff goal during any season, and which seasons it was. If you decide to double check me, beware that some players appear to have 20+ year gaps, because multiple players can have the same name (like Syl Apps!).
Here is a table of all 9+ year gaps: