Leasing of financial instruments?

Is there a way to trade financial instruments (whatever instrument it may be) on a lease basis - and accordingly receive a premium back? Either fixed or flexible, or even "maybe receive" a premium back on a financial instrument?

I have thought about this method as a diverse way of investment but I havent been able to find anything.

I'm not sure what you're asking, but almost all trading is "leased" in some manner, if only because of the implicit leverage.

Well to simplify it:

Instead of buying a share in a company, I am leasing the share, and I am getting the dividend on it (or whatever special rights the share would give me). But what I am looking for is probably a purchase-hire, more like a monthly lease price I have to pay in order to receive something back on my financial instrument. I am of course looking to lease the instrument instead of buying because its much cheaper (in the short run) to lease.

I don't see why it shouldn't be possible in theory; in fact short selling that isn't naked is done by a similar arrangement.

But I'm not familiar with it in practice. Others more knowledgeable will no doubt reply