Yes but Tenerife does not have the power to control its borders, that is for the national government of Spain, as was shown a few days ago when they overruled Tenerife allowing antigen tests for entry, so I have no idea what is going on.
The Canarian government site is self contradictory if Google translate is accurate.
https://www3.gobiernodecanarias.org/noticias/el-gobierno-de-canarias-acuerda-limitar-la-entrada-y-salida-de-personas-de-tenerife/It starts with:
In the case of national and foreign tourists who plan to come to the island of Tenerife on vacation, they can avail themselves of the exceptionalities contemplated by the current regulations on the right of admission in tourist accommodation establishments, where a negative health test must be presented that accredit being free of coronavirus.
But also says:
The entry and exit of people to the island of Tenerife is restricted from midnight on December 18 (Friday) to January 1, 2021 and it is also recommended to avoid mobility between its municipalities. The restriction applied to Tenerife will apply except for those adequately justified trips that occur for any of the following reasons contemplated in article 6 of Royal Decree-Law 926/2020, of October 25, the rule that declares the state of alarm in the country to contain the spread of infections caused by SARS-CoV-2:
Assistance to health centers, services and establishments.
Compliance with labor, professional, business, institutional or legal obligations.
Attendance at university, teaching and educational centers, including nursery schools.
Return to the place of habitual or family residence.
Assistance and care for the elderly, minors, dependents, people with disabilities or especially vulnerable people.
Travel to financial and insurance entities, or to refueling stations in neighboring territories.
Required or urgent actions before public, judicial or notarial bodies.
Renewals of permits and official documentation, as well as other administrative procedures that cannot be postponed.
Taking official exams or tests that cannot be postponed.
Due to force majeure or situation of need.
Any other activity of a similar nature, duly accredited.