"allowing an exception" is correct and usable in written English.
You can use it when referring to an allowance or exemption from a rule or limitation. For example, "The student was allowed to take the exam late, allowing an exception to the policy of no late submissions."
Many of the arguments Monday concerned whether the court should strike down all of the Michigan statute or just the part allowing an exception for claims of fraud.
Allowing an exception to the rule against pretrial appeals in criminal cases for speedy trial claims would threaten precisely the values manifested in the Speedy Trial Clause.
Malebranche himself, in his last published work, says explicitly that the human soul is the "true" and "real" cause of its own free consent to "the motives that solicit the soul," thus allowing an exception to his general principle that God is the only true efficient cause (Réflexions sur la Prémotion physique, OM, 16:42–43).
Malta is the only European country that bans abortion in all cases, not even allowing an exception when the woman's life is in danger, according to abortion-clincs.eu.eu
As will be explored in Section 4, some European countries have chosen to enact legislation allowing an exception to privacy in the context of medical research whenever there is a serious risk to the health or life of a family member.
Ross's show has been allowed an exception for Cresswell.
The idea was to allow an exception for teenagers who were pregnant.
Nonetheless, when he had to, Dulles allowed an exception, one that has remained largely hidden.
The agreement allowed an exception, though, for employees who turned 50 by July 1 of that year.
In cases where turning over evidence might endanger a witness, for example, a judge could allow an exception.
White House officials said they hoped that the House Rules Committee would allow an exception to the rules, so Democrats could offer an alternative costing $100 billion over five years.
