The results of the meta-analysis published by Francisca van Steensel & Emma Heeman  (open-access) on the topic of anxiety levels in children diagnosed with an autism spectrum disorder (ASD) should not really be a surprise to anyone.
Concluding a few things based on the analysis of the peer-reviewed literature in this area - 83 articles on the topic - the main points were that "anxiety levels of youth with ASD are much higher compared to typically developing children" and further that "as IQ increases, so does the difference in anxiety levels between ASD and typically developing children" (age also showing a similar relationship to that of IQ). The authors suggest that quite a bit more investigation is required on this topic not least in areas such as managing/treating anxiety issues in the context of autism, distinguishing anxious signs and symptoms from the traits of autism and importantly noting "the impact of anxiety for the daily functioning—not only for the children themselves, but also for the family." I might add that at least one of these authors has some research form when it comes to looking at the complicated relationship between autism and anxiety (see here).
I've covered anxiety and autism on this blog more times that I can remember (see here and see here for examples). I hope I'm not too forward in saying that various types of anxiety disorder do appear to be over-represented when it comes to a diagnosis of autism and that anxiety can sometimes (day-to-day) be more disabling to a person that the presentation of their autism.
What's missing from the van Steensel / Heeman analysis? Well I might suggest two things. First, a realisation that in these days of 'autism rarely appearing in a diagnostic vacuum' (see here) some of the other comorbidity over-represented in relation to autism might also be important to the presentation of anxiety. I'm thinking specifically about the quite nebulous term 'depression' as being one prime example (see here) but there may be others too (see here). Second, and also potentially related to the first point is the idea that somatic features might also be an important part of a relationship between anxiety and autism. I've just mentioned about depression and anxiety perhaps not being unstrange diagnostic bedfellows, well, things like gastrointestinal (GI) issues can be part of that relationship too (see here for example). We can argue all day about whether anxiety is a cause or effect of physiological issues (with and without autism in mind) but there is a growing evidence base to suggest that psychology and the somatic are not necessarily totally independent systems.
As to the question of treating/managing anxiety when it occurs with autism, the authors mention about the potential usefulness of something like cognitive behavioural therapy (CBT) as one avenue (see here). One could also entertain the use of more pharmacotherapeutic strategies too; bearing in mind the need for good medicines management and a focus on minimising any side-effects. I'd also draw your attention to another avenue gaining some research traction: exercise (see here). Acknowledging that participation in physical activity can sometimes be a bit of an issue when it comes to autism (see here for example), there is no reason to suggest that what might work for the population at large in terms of 'exercise for anxiety' should not be equally applicable to presented anxiety in the context of the autism spectrum. Indeed, added to other potentially positive outcomes associated with exercise use with autism in mind (see here) , I'd very much like to see a lot more research conducted on this potentially important area.
 van Steensel FJA. & Heeman EJ. Anxiety Levels in Children with Autism Spectrum Disorder: A Meta-Analysis. J Child & Family Studies. 2017; 26: 1753.