After a brief return to England, Kempe accompanied two other future Lord Chamberlain's Men, George Bryan and Thomas Pope, to Elsinore, Denmark, where he entertained Frederick II. He appears not to have remained long in Elsinore, but his whereabouts in the later 1580s are not known.
That his fame was growing during this period is indicated by Thomas Nashe's An Almond for a Parrot (1590), which Nashe dedicates to Kempe, calling him "vicegerent general to the ghost of Dick Tarlton." The title-page of the quarto of A Knack to Know a Knave advertises Kempe's "merriments"; because title-pages were a means to draw attention to a book, the mention of Kempe suggests that he had become an attraction in his own right. Critics have generally viewed the scene in which Kempe performs as rather flat (Collier, 97); it is assumed that the scene provided a framework within which Kempe could improvise. Entries in the Stationers' Register indicate that three jigs perhaps written by Kempe were published between 1591 and 1595; two of these have survived.
By 1592, and perhaps earlier, Kempe was one of Lord Strange's Men; he is listed in the Privy Council authorization for that troupe to play seven miles out of London. In 1594, upon the dissolution of Strange's Men, Kempe, along with Richard Burbage and William Shakespeare, joined the Lord Chamberlain's Men. He remained with the company until near the end of the century, when a still-unclear sequence of events removed him from the company. Early in 1599, the Burbages included him as a sharer in the plans to construct the Globe Theatre. At some point during the year, he resumed his solo career.
In February and March of 1600, Kempe undertook what he would later call his "Nine Days Wonder", in which he morris danced from London to Norwich (a distance of over a hundred miles) in a journey which took him nine days spread over several weeks, often amid cheering crowds. Later that year he published a description of the event in order to prove to doubters that it was true. (The year he gives was 1599 Old Style, which has caused some later confusion. That Kempe's jig took place in 1600 (New Style) is established by a record of the payment of his prize money by the Norwich City Corporation.)
Kempe's activities after this famous stunt are as obscure as his origins. On evidence from The Travels of the Three English Brothers, Kemp is assumed to have made another European tour, perhaps reaching Italy; by 1601, he was borrowing money from Philip Henslowe and had joined Worcester's Men. The last undoubted mention of him occurs in Henslowe's diary in late 1602. Parish records record the death of "Kempe, a man" in St. Savior, Southwark, late in 1603; while this is not clearly the comedian, the record fits his departure from the documentary record.
As an actor, Kempe is certainly associated with two roles: Dogberry in Much Ado About Nothing and Peter in Romeo and Juliet. (In the quarto text of the latter, and in both quarto and First Folio text of the former, he is identified in speech prefixes and stage directions.) From these hints, a list of Kempe's parts has been deduced which, if conjectural, is not improbable: Costard in Love's Labours Lost, Bottom in A Midsummer Night's Dream, Lancelot Gobbo in The Merchant of Venice, and Cob in Ben Jonson's Every Man in His Humour. Falstaff is a more ambiguous case. Though Falstaff presents some features of an Elizabethan dramatic clown, his character is higher in class and more complex than the other roles with which Kempe is associated.