"strict obedience" is correct and usable in written English.
It can be used to refer to a situation where someone (or a group) is expected to strictly follow a set of rules, expectations, or instructions. For example, "I expect strict obedience of my students in my classroom."
Within the organization, there's a tradition of strict obedience to superiors.
However, it has a history of strict obedience to Mr Chávez's wishes.
Hard work, proper training and strict obedience are the keys, he gruffly insists.
Strict obedience to the religious law and imitation of the Prophet were basic for the mystics.
Former members of the group said that its leaders, who believe they are anointed by God, demanded strict obedience from the group.
His view that judges should interpret the law is a challenge to the principle of strict obedience to its letter that prevailed during the dictatorship.
There Baba began his practice of demanding strict discipline and obedience from his disciples.
These two theocratic regimes on opposite sides of the Gulf are linked by their obedience to strict Islamic law, the one Sunni, the other Shia.
Even the religious hierarchy has slowly moved away from the strict Wahhabist doctrine of obedience to the sovereign, and some of its members now argue for setting limits to his rule.Events in the neighbouring emirate of Qatar have also jolted Saudi minds.
Doubts over the company's future prompted the family in 2017 to agree to a major investment and modernisation programme and an end to the company's traditional practice of operating according to strict rules governing order and obedience.
When teachers are overworked, they have to save energy by performing their daily tasks "mechanically", and in order to do this they impose a strict order and demand pupils' obedience to it.
