Bulkify the Logic

public class LeaveRequestTriggerHandler {
    public void beforeInsert(List<Leave_Request__c> newRequests) {
        Set<String> employeeNames = new Set<String>();
        for (Leave_Request__c req : newRequests) {
            employeeNames.add(req.Employee_Name__c);
        }

        List<Leave_Request__c> existingRequests = [
            SELECT Id, Employee_Name__c, Start_Date__c, End_Date__c
            FROM Leave_Request__c
            WHERE Employee_Name__c IN :employeeNames AND Status__c != 'Rejected'
        ];

        for (Leave_Request__c newReq : newRequests) {
            for (Leave_Request__c existing : existingRequests) {
                if (newReq.Employee_Name__c == existing.Employee_Name__c
                    && datesOverlap(newReq.Start_Date__c, newReq.End_Date__c, existing.Start_Date__c, existing.End_Date__c)) {
                    newReq.Start_Date__c.addError('This leave request overlaps with an existing request.');
                }
            }
        }

        for (Integer i = 0; i < newRequests.size(); i++) {
            for (Integer j = i + 1; j < newRequests.size(); j++) {
                Leave_Request__c reqA = newRequests[i];
                Leave_Request__c reqB = newRequests[j];
                if (reqA.Employee_Name__c == reqB.Employee_Name__c
                    && datesOverlap(reqA.Start_Date__c, reqA.End_Date__c, reqB.Start_Date__c, reqB.End_Date__c)) {
                    reqB.Start_Date__c.addError('This request overlaps with another request in the same submission.');
                }
            }
        }
    }

    private Boolean datesOverlap(Date startA, Date endA, Date startB, Date endB) {
        return startA <= endB && startB <= endA;
    }
}

Every lesson from this module combined into one working class — one query, two purely in-memory comparison passes, one shared helper method.

Inserting 50 Leave_Request__c records across 10 different employees at once: one SOQL query fetches every existing request for those 10 employees; the new-vs-existing comparison loop runs at most 50 × (however many existing requests those 10 employees have) — pure in-memory work; the new-vs-new comparison runs at most 50 × 49 / 2 pair checks — also pure in-memory. Total SOQL queries: 1, regardless of whether the batch was 5 records or 200.