Start a tree-care enquiry with what you have observed and where the tree stands. Describe a branch over a route, a change in the canopy or a concern about the space around the trunk. Keep that observation separate from a diagnosis or a proposed treatment.
Give the tree a clear location
A photograph of the whole tree and a wider view of its surroundings https://www.youtube.com/channel/UCOikoYu_9U58tVGibAgkezg can make the discussion easier to follow. Label each image so two trees in the same garden are not confused. Note when you first noticed the concern and whether you have photographs from an earlier date.
Turn the observation into questions
Ask what needs to be assessed before work is proposed, how the recommended scope will be explained and what information you should keep afterwards. If several trees need attention, identify each one separately in the enquiry. A brief that distinguishes the trees and the questions gives you a useful starting point for reviewing a later quote.