In your specific case, guessing at what your code likely includes, the objects will probably be deallocated when you want them to be. That's a lot of "guessing," "likely," and "probably." You really need to understand how the memory management works in order to reason about it.
If the AVAudioPlayer is strongly referenced by anything else, then it won't be released until those strong references are gone. In other words, setting thePlayer won't deallocate the player if something else has a strong reference to it. (That "something" may be some part of the system frameworks, or even itself in some rare cases. It doesn't have to be your code.)
If the AVAudioPlayer has pending autorelease calls on it, then it won't be released until the autorelease pool drains (usually at the end of event loop, which basically means "when your method that UIKit called returns.") For example, if you create a large number of objects in a loop and immediately throw them away, they may or may not be deallocated until the autorelease pool drains. Again, autoreleases may be injected by system frameworks. In practice, this means that the object will usually be deallocated "soon" (in a small fraction of a second), but not necessarily immediately. You can clean up autoreleased objects sooner by using @autoreleasepool blocks, which is sometimes necessary if you create many temporary objects in a loop. This is not needed very often.
But to a first-order approximation, in many of the most common cases, yes, replacing the property will automatically and immediately deallocate the previous object.