Yes, in many cases. Moving from a student residence permit to a work permit is possible provided you meet the conditions for a new residence permit based on employment.
In practice that means a job offer from a Danish employer, in a position that satisfies one of the schemes, commonly the Supplementary Pay Limit Scheme.
The reason this question comes up so often is that the answer depends on details: the type of job, the salary on offer, and the residence status you currently hold. Those three between them decide which scheme applies and whether the switch works at all, which is worth establishing before you hand in a notice or sign anything.