Can you please tell me if I need to use the before payment in the context below?
I'd like to know if you are going to be the one taking care of (the) payment for our services.
Is the use of the optional there, if so, which one is more common?
If you are talking about one specific payment for your services, you would use the definite article 'the'. We use a definite article when we are talking about one single specific thing.
I'd like to know if you are going to be the one taking care of the payment for our services which is due by the end of this month.
If you are talking about the whole matter of payment more generally, perhaps over a period of time, and involving more than one transfer of funds, you could omit the definite article.
I'd like to know if you are going to be the one taking care of payment for our services during the period of the five-year contract which has now been signed.