Add new option in runtime to already registered HttpClient service

Question

In the startup of application I regiseter a new HttpClient named AmadeusSearchClient.

services.AddHttpClient<AmadeusSearchClient>(options =>
    {
        options.BaseAddress = new Uri(configuration.GetSection("AmadeusApi:BaseAddress").Value);
        options.Timeout = new TimeSpan(0, 0, int.Parse(configuration["AmadeusAccessToken:Timeout"]));
    });
    return services;

I'm receiving Amadeus access token using my other HttpClient called AmadeusAccessTokenClient, also registered in DI.

services.AddHttpClient<AmadeusAccessTokenClient>(options =>
    {
        options.BaseAddress = new Uri(configuration.GetSection("AmadeusApi:BaseAddress").Value);
        options.Timeout = new TimeSpan(0, 0, int.Parse(configuration["AmadeusAccessToken:Timeout"]));
    });
    return services;

To properly use AmadeusSearchClient, I need to add access token in the header of my request.

cancellationToken.ThrowIfCancellationRequested();

        var message = new HttpRequestMessage(
            HttpMethod.Get,
            "v1/travel/analytics/air-traffic/busiest-period?cityCode=BOS&period=2017");

        _httpClient.DefaultRequestHeaders.Add("Authorization", $"Bearer {_token.Get()}");

        var response = await _httpClient.SendAsync(message, cancellationToken);

        var res = await response.Content.ReadAsStringAsync();

As you can see, in every request I have to add _httpClient.DefaultRequestHeaders.Add("Authorization", $"Bearer {_token.Get()}"); DefaultRequestHeader manually. Is there any way to update the options of already registered AmadeusSearchClient when my application receives access token using AmadeusAccessTokenClient service?