The correct option is
A hired
The given sentence is interrogative, 'You' being the subject and 'met' being the verb. The 'secretary' is the object of the verb, and the phrase that follows describes this object, by giving more information about it.
Option A: 'Hired' is a contraction of 'who was hired'. The words 'who was' when omitted, the meaning of the sentence remains unchanged. The clause 'who was hired last week' is a relative clause ('who' is a relative pronoun) that defines the noun 'secretary'. Hence this option is correct.
Option B: 'She was hired' is an independent clause that would begin a sentence, but it does not define the noun 'secretary'. A relative pronoun like 'who' is required that relates the noun to the sentence. The pronoun 'she' does not function the same way.
Option C: 'Was hired' also does not define the noun. 'Was hired' is a verb phrase that cannot describe a noun.
Option D: 'When she was hired' is a time-related clause and does not function as a defining clause.
Hence options B, C and D are incorrect.