Hi, I’m a retired chess coach.
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1500 ELO is certainly a decent rating compared to the entire chess population.
(I couldn’t find the FIDE rating percentiles on their website - I presume chess.com has access to the full rating list.) -
I’m certain that it’s easier to shoot up in strength when you are younger. My first ever rating (aged 13) was 1825 and a year later I reached 2050. (By 18 I was rated 2200.)
I think it would be very hard to jump from 900 - 1500 in one year aged 52.
But I’m confident you could get there in a few years! -
I’m sure a chess coach would help.
Also playing a lot and analysing every game afterwards is essential.
Computers will be most useful (as available opponents / excellent analysts / opening repetoire.) -
A good way to start is to practice endgames. There are far less pieces to consider and you can learn about the different strengths and weaknesses of each piece.
If you don’t know already, you could learn some basic checkmates (King +2 rooks v King; King + Queen v King; King and Rook v King: King and 2 bishops v King.) -
For a follow-up, learn tactics (pin, fork, discovered check, skewer, overload etc.) These do come up regularly and it’s important you can both play them and avoid walking into them.
Note that all the above involves spotting patterns and that is a big part of chess. -
By all means use computer databases / game collections to study openings. I recommend you only play a few, so you can understand what to do.
DO NOT MEMORISE OPENINGS! As soon as an opponent plays an unusual move, you are in a world of trouble. But with the aforementioned understanding, you can cope.
If you’d like I can help a bit.
I can analyse one or two of your games and also play a practice game with you (both on the board.)
See Chess training game between glee and NAF1138 - Thread Games - Straight Dope Message Board for an actual game thread and
Chess training game between glee and NAF1138 - comments etc - The Game Room - Straight Dope Message Board for the accompanying discussion thread.