Atomic clocks, the most accurate instruments in existence, are reaching new levels of precision. These devices now find novel uses-from the exploration of relativity [1] to the detection of dark matter [2, 3]-all from same principle: measurement of the frequency of the light that excites a reference atomic transition. The ²S_1/2 (F 0) → ²F_7/2 (F 3) electric octupole (E3) transition in ¹⁷¹Yb⁺, with its Δν ≈ 1 nHz [4] linewidth and low sensitivity to external electromagnetic fields, lends itself to this usage [5]. We probe this transition in a single ¹⁷¹Yb⁺ ion held in a newly-designed endcap RF trap [6]. This design achieves a low temperature rise of 0.14(14)K. Excess micromotion in the trap is automatically compensated, resulting in a fractional frequency uncertainty of the combined RF-Stark and 2^nd order Doppler shifts of 3.6 × 10⁻¹⁹. Anomalous phonon heating rates in the radial plane were measured as (−4.9 ± 5.2) s⁻¹ and (−1.3 ± 3.6) s⁻¹ for secular frequencies of 446 kHz and 470 kHz. The ion's differential polarisability at λ = 7 μm has been measured, suggesting a reduction in the BBR-related systematic error of the electric quadrupole (E2) transition by a factor of 5 and confirming the results of a previous measurement for the E3, performed using a different method [7]. However, a limitation prevented full confidence in our uncertainty levels. To pre-stabilize the frequency of our laser a 28 cm long, ultra-stable Fabry-Pérot cavity was constructed and used to drive the E3 atomic resonance with a linewidth of 1.64(2) Hz. Its finesse was measured as 458 000 and, in an atomic lock, a clock stability of 1.9 × 10⁻¹⁵ (τ/1 s)^−1/2 was observed. The laser's frequency was measured and its stability transferred to other wavelengths via a femtosecond optical frequency comb. An international clock comparison campaign was carried out via satellite-mediated microwave links: the first of its scale, involving 4 National Measurement Institutes (NMIs) and 5 optical atomic clocks. A new technique was developed to analyse the resulting data and to characterize its uncertainty. The lowest fractional uncertainty in the comparison between any pair of clocks was 2.8 × 10⁻¹⁶. Finally, an absolute measurement of the E3 transition has been carried out through a link to International Atomic Time (TAI), without a local primary standard. The transition frequency was measured to be 642 121 496 772 645.17(22) Hz: the best measurement of this transition to date [8, 9].