"Its" refers here to "xxx's": the publicity materials of xxx, which is receiving the sponsorship.

"Cartelería" can refer specifically to posters, "carteles", but it usually includes a broader range of materials including leaflets, fliers, press releases, and even TV ads, for example. "Signage" can sometimes be the right word, though that normally refers to signs that are displayed to give directions.

I think the idea here is along the lines Anne suggested. There are different levels of sponsors, presumably depending on how much sponsorship they provide. Those who give most are "recognised" (this is the usual expression) on xxx's posters etc.: their names and logos are displayed and their sponsorship is acknowledged. Others, who give less, don't get this advantage, though their sponsorship will be acknowledged in less prominent ways. After all, commercial sponsorship amounts to buying publicity for the sponsor, and the more you give, the more publicity you get. So those who give most have to receive some relative privilege compared to those who give less.

If it is possible to check with the client just what "cartelería" includes here, that would be useful, but by default I would put a standard general term like "publicity materials".

"Party Sponsor $2,000 exclusive or $1000 or $500 shared cocktail party sponsorship includes recognition in all publicity materials [...]"
http://www.akronbar.org/Files/Events/2012/Golf Outing 2012 S...

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Note added at 9 hrs (2012-06-13 08:46:29 GMT)
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I think the subject of "dan presencia" is "niveles"; in other words, level X/Y/Z sponsorship gives you a presence on the publicity (or display) materials: your name and logo appear on them. That is what you get for being a level X/Y/Z sponsor. So by implication, being a sponsor at another level does not give you that presence: your name and logo do not appear (but you get some other kind of lesser advantage).

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Note added at 9 hrs (2012-06-13 08:56:37 GMT)
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I think I've identified what this refers to, but I won't give details so as not to violate confidentiality. From what I have seen, "cartelería" actually refers specifically to "carteles" (large and small), so in fact I think you could say "on the posters". But also, this confirms the meaning of "dan presencia"; there'e another comment about the same thing which says: "La contratación de stand o regalo en bolsa no da derecho a presencia cartelería". So "dar presencia" means "dar derecho a presencia".

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Note added at 9 hrs (2012-06-13 09:00:32 GMT)
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My revised proposal would therefore be:

those [niveles] that give sponsors/collaborators the right to appear on the posters