"Further reassurance" means additional comfort or encouragement given to someone to make them feel more secure or less worried about a particular situation. Full definition
This gives further reassurance of the quality and safety of your chosen provider. (educationbusinessuk.net)
Show the expertise behind your logo: An About page offers further reassurance, as does a team section where you introduce yourself and your staff. (creativeboom.com)
For further reassurance, check your child's growth and weight charts, or check with your child's pediatrician. (childdevelopmentinfo.com)