"To delay the start" means to postpone or hold back the beginning of something, either intentionally or due to circumstances, so that it doesn't happen or begin as planned. Full definition
Instead of delaying the start of your job search AND the start of a new job, hire a pro to help you in preparing the best product in a reasonable timeframe. (careerresumes.com)
In addition, the administration supported informal peer check - ins after students went home for the day by delaying the start time of after - school staff meetings. (edutopia.org)
By delaying the start date of your coverage, these companies are able to decrease their liabilities and lure people in by charging a low introductory rate. (termlifeadvice.com)