German term (edited): Spezialit�tsvorbehalt

... gained extradition proceedings.
It seems to be part of Swiss law. If Germany applies for extradition of a suspect for a particular crime, Switzerland can agree to deport the person, but on condition that the information gained during the extradiction proceedings cannot be used to prosecute any other crime.
So if the extradiction is for prosecution in a criminal court, the evidence cannot be used to prosecute the suspect for tax evasion or similar.
See http://www.strafo.de/archivver/aufsatzkaligin.htm (and other Google hits).
The Oxford Dic of Law says:
"(extradition treaties between states)... invariably contain the following three features:
(1) (prima facie evidence of guilt) (2) (no political offenders)
(3) no surrender will be made unless adequat e assurances are given that the accused will not on that occasion be tried for any offence other than the crime for which he is surrendered"

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Note added at 53 mins (2005-06-15 08:04:44 GMT)
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The person pursued may be extradited only on condition that the requesting State:
a. shall neither prosecute nor sentence nor re-extradite hint to a third State for any offence committed prior to his extradition and for which extradition was not granted;
b. shall not deprive him of his liberty on any other pre-existing ground;
c. shall not bring him before an extraordinary court;
from the Swiss FEDERAL ACT ON INTERNATIONAL MUTUAL ASSISTANCE IN CRIMINAL MATTERS (IMAC) at:
http://www.unodc.org/unodc/en/legal_library/ch/legal_library...

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Note added at 1 hr 17 mins (2005-06-15 08:29:04 GMT)
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To sum up what I gather from Google:
Spezialitätsvorbehalt = the requirement that any prosecution which takes place as a direct result of the extradition may only be for the offence stipulated in the application for extradition, and that any evidence gained in the extradition proceedings may not be used to prosecute other offences.
So for your sentence quoted in the question:
\"extradition (would/could/may?) only be granted subject to a restriction on any resulting prosecution, so that the appellant must not be prosecuted for treason or ...\"