Round the clock means all day and all night without pause. Work round the clock, round the clock care.
It describes effort rather than hours precisely, since nobody literally works twenty-four hours. Round the clock care means somebody is always there rather than one person always awake.
1phraseround the clockAll day and all night without pause.
“The crews worked round the clock for a week to reopen the line.”
round the clock is a phrase.
Practised in Time & Calendar