I'm only 2 years into shooting competitively and have managed to secure a few sponsor's.
A cartridge company, gun shop, chokes and another company all help out.
Most cartridge sponsorships are only a 10% - 20% discount and then you are stuck using only the the cartridges they offer you.
I am very lucky that Lyalvale Express offered me a very generous contract and I'm able to choose any of their compertition cartridges I choose.
All my sponsor's found me!
I won a good few major events and each time I recored them on a CV type document.
After winning my class at the Essex Masters, English Open, Beretta Worlds, Benelli SP'Auto, and was leading the Premier League (ended up joint second and in a shoot off with Richard Faulds who beat me by 1) and many other events in my first year, Express emailed asking if I'd sent a CV with the possibility of joining their team.
It's not all about winning either!
It's your image,
How you dress
How you act
Are you polite
Do you loose your temper
Argue with ref's
Etc etc
They don't want someone who is a great shot that looks scruffy and causes a seen.
Sponsor's want someone out representing their brand professionally.
Phone the cartridge companies and speak to them! Ask what they look for and if they'd look at your cv.
Most of the sponsorships run from Jan / Feb so they'd have a year to follow your scores.
Also get your instructor to give a reference if you have one, even the ground owners or staff.
Everything will help.
Best of luck in the future