There is a Get version of SingleTickerProviderMixin that implements the TickerProvider intreface (using the same Ticker class from the Flutter SDK).

It has a nice name: GetSingleTickerProviderStateMixin.

(Updated on December 21, 2020: SingleGetTickerProviderMixin is deprecated in the latest GetX. Thanks to the commenter who pointed this out.)

The example below is essentially from the Flutter documentation for TabController.

From the StatefulWidget of the linked example, I ported its contents to a GetxController (MyTabController) and added the mixin GetSingleTickerProviderStateMixin:

class MyTabController extends GetxController with GetSingleTickerProviderStateMixin {
  final List<Tab> myTabs = <Tab>[
    Tab(text: 'LEFT'),
    Tab(text: 'RIGHT'),
  ];

  TabController controller;

  @override
  void onInit() {
    super.onInit();
    controller = TabController(vsync: this, length: myTabs.length);
  }

  @override
  void onClose() {
    controller.dispose();
    super.onClose();
  }
}

To use MyTabController in a stateless widget:

class MyTabbedWidget extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    final MyTabController _tabx = Get.put(MyTabController());
    // ↑ init tab controller
    
    return Scaffold(
      appBar: AppBar(
        bottom: TabBar(
          controller: _tabx.controller,
          tabs: _tabx.myTabs,
        ),
      ),
      body: TabBarView(
        controller: _tabx.controller,
        children: _tabx.myTabs.map((Tab tab) {
          final String label = tab.text.toLowerCase();
          return Center(
            child: Text(
              'This is the $label tab',
              style: const TextStyle(fontSize: 36),
            ),
          );
        }).toList(),
      ),
    );
  }
}

Another workaround is DefaultTabController, which is useful if you don't need to control the state of the TabBar and TabView widgets.

class MyDemo extends StatelessWidget {
  final List<Tab> myTabs = <Tab>[
    Tab(text: 'LEFT'),
    Tab(text: 'RIGHT'),
  ];

  @override
  Widget build(BuildContext context) {
    return DefaultTabController(
      length: myTabs.length,
      child: Scaffold(
        appBar: AppBar(
          bottom: TabBar(
            tabs: myTabs,
          ),
        ),
        body: TabBarView(
          children: myTabs.map((Tab tab) {
            final String label = tab.text.toLowerCase();
            return Center(
              child: Text(
                'This is the $label tab',
                style: const TextStyle(fontSize: 36),
              ),
            );
          }).toList(),
        ),
      ),
    );
  }
}