The 'skill sets' and 'personality traits' referred to in the sentence are indicated using the relative pronoun 'that'. The correction is 'that give us high competence'.
When 'hope' is in the present tense, it is followed by 'will' and not 'would'. 'Concede' is always followed by 'to' and not 'with'. Employees is a plural noun indicated by the preposition 'their'. Hence the correction is 'the management will concede to their demands'.