If you own property in Phuket such as a condo you might want to place it on the market to rent it to expats or tourists. There will be the need for a lease agreement in Thailand however there are also other issues. You can rent out the property however your agent would have to deduct withholding tax from the rent before paying it into your account.
You do not need to hold a visa in order to pay tax. With regards to personal income tax on earnings in Thailand, you should talk to a Thai tax consultant. Taxpayers are classified into “resident” and “non-resident”. “Resident” [for tax purposes] means any person residing in Thailand for a period or periods aggregating more than 180 days in any tax year.
A resident of Thailand is liable to pay tax on income from sources in Thailand on a cash basis, regardless of where the money is paid, as well as on the portion of the income from foreign sources that are brought into Thailand. A non-resident is, however, subject to tax only on income from sources in Thailand.
Some banks will also not allow you to open a Thai bank account without a work permit and many will not allow you to open a Thai bank account without a Thai visa. Some do allow you to open an account with a visa on arrival in your passport so check which banks in Phuket will allow you to open a bank account. It is much easier to draw you rental payments with an ATM card around the world from your Thai bank account.