If you are paying for signage relating to your business and getting nothing else in return, that would be advertising and a deductible expense. However, if you get other benefits e.g club membership, food and drink, function attendance or playing rights as part of a package, some of the expenditure would be entertainment and not tax deductible.
Two ATO references to sports related expenditure are are TR 92/162 and ATO ID 2005/286. If you are are purchasing a sponsorship package, including entertainment, ask the club if they are able to give any guidance on valuing the different components.