Which ITIL guiding principle recommends using existing services, processes and tools when improving services?

The ITIL guiding principle of start where you are advises service providers to avoid starting from scratch when improving services, but rather to assess the current state and use existing services, processes and tools as a basis for improvement. This principle helps to avoid wasting resources, reinventing the wheel, or losing useful elements of the current state. It also helps to identify and leverage the strengths, weaknesses, opportunities and threats of the current situation. References:

ITIL 4 Managing Professional Transition Module, page 16

ITIL 4 Foundation: Complete Course with 2 Practice Exams, section 3.2.3

The 7 Guiding Principles of ITIL 4 - IFS Blog, paragraph 2

The 7 ITIL 4 Guiding Principles: Explained in Detail, paragraph 5