Notice [or summons] shall be served upon the appointed expert in order for him or her to submit estimates of their [hourly,legal, consulting] fees, which shall be collected/disbursed by the petitioners/ claimants/ within 20 days.

Several alternatives: take your pick, and good luck with your project.

in.ti.mar
[ïtim'ar] v. to summon, cite, convoke

Legal documents usually "cite"

Cite:
(1) To command the presence of a person; to notify a person of legal proceedings against him and require his appearance in the court, especially to face contempt proceedings. (2) To read or refer to legal authorities in an argument or submission to a court. For example, to cite a case is to refer to a particular case in an attempt to persuade the Court to be guided by the decision reached in that case.
http://www.thelegaldictionary.com/legal-term-details/Cite

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Note added at 12 hrs 29 mins (2004-12-03 16:56:14 GMT)
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convoke
\\Con*voke\"\\, v. t. [imp. & p. p. Convoked; p. pr. & vb. n. Convoking.] [L. convocare: cf. F. convoquer. See Convocate.] To call together; to summon to meet; to assemble by summons.
http://dictionary.reference.com/search?q=convoke

The expert appointed [by the court] is ordered to present his fee proposal, said fees to be paid by the plaintiffs within a period of 20 days ...