Hello I am a solicitor with over 15 years experience. I will try to hep you with this.
It sounds like you are describing a type of retainer relationship. A client can pay a regular (usually monthly) fee and in exchange the lawyer agrees to be constantly available for the client. Sometimes there will be an agreement as part of this not to act for named others. Solicitors are happy to enter into these agreements as it holds out the possibility of being paid for doing nothing.