Is there a word that means "render dependent on"?

Engender or Enjoined is the word.

To enjoin them to buy from you is to cause or create a need for them to buy from only you. It is more polite than enslave but amounts to the same thing. So long as they need a product they will look to you. I hope you can be happy in serving them.

I know no such word as you suggest. Two words come to mind:

You have ensnared them.

Ensnare = to catch or get control of something or someone:

Cambridge Dictionary

You may also have enticed them.

Entice = to persuade someone to do something by offering them something pleasant

Cambridge Dictionary

Which to choose? ensnare fits your example better.

I point out that you may ensnare (in a new contract) by enticing (with an attractive offer), but that you are unlikely to entice by ensnaring.